Finite Group Databasebeta

← #14654233

Subgroups — #14654233

Order 2816.

692 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622646C211yesmaximal, characteristic, complemented
2#13073088C211yesmaximal, characteristic, complemented
3#13069453C211yesmaximal, characteristic, complemented
4#13068703C211yesmaximal, characteristic, complemented
5#13067184C211yesmaximal, characteristic, complemented
6#13066463C211yesmaximal, characteristic, complemented
7C11×#3186C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C2×C11×#121C2211yescharacteristic
10C2×#66988—22no—
11C22×C4⋊Dic11C2211yescharacteristic
12C11×#480—21no—
13C11×#480—21no—
14C11×#466—22no—
15C11×#447—21no—
16C11×#447—21no—
17C2×C11×C22⋊C8C2211yescharacteristic
18#10622834—21no—
19C2×#66898—22no—
20C2×#66896—21no—
21#10622825C2211yescharacteristic
22C4×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24#10622646—22no—
25#10622646—22no—
26#10622589—21no—
27C2×#66871—21no—
28#10622562—22no—
29#10622189—22no—
30#10622175—22no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D411yescharacteristic
34C22×D4×C11D411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×Dic11—21no—
37C2×C11×D8—22no—
38C22×C8×C11D412yes—
39C11×#121—21no—
40C11×#121—21no—
41C11×#121—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#121—21no—
45C11×#121—21no—
46C11×#121—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C22⋊Dic11—24no—
52C2×C22⋊Dic11—21no—
53C2×C22⋊Dic11D412yes—
54#66988—44no—
55#66988—44no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11D412yes—
63C2×Dic11⋊C4—24no—
64C2×C4×Dic11—21no—
65C22×C11⋊C8—21no—
66C11×#107—22no—
67C11×#102—22no—
68C11×#102—22no—
69C11×C22⋊C8—21no—
70C11×C22⋊C8—21no—
71#66898—44no—
72#66896—24no—
73C11⋊#95—21no—
74C11⋊#95—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)D412yes—
77#66871—24no—
78#9952—111nomaximal, Sylow
79C24×C11—21no—
80C24×C11—21no—
81C24×C11C2×D411yescharacteristic
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—42no—
87C2×D4×C11—42no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—42no—
93C2×D4×C11—42no—
94C2×D4×C11—42no—
95C2×D4×C11—42no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—42no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×Dic11—22no—
106C22×Dic11—22no—
107C22×Dic11—41no—
108C22×Dic11—41no—
109C22×Dic11—41no—
110C22×Dic11—42no—
111C22×Dic11—42no—
112C11×D8—82no—
113C2×C8×C11—22no—
114C2×C8×C11—42no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C22⋊Dic11—22no—
124C22⋊Dic11—48no—
125C22⋊Dic11—42no—
126C22⋊Dic11D814yescomplemented
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—42no—
130C4⋊Dic11—41no—
131C4⋊Dic11—41no—
132Dic11⋊C4—48no—
133C4×Dic11—42no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—42no—
136#3186D1111yescharacteristic
137C2×#480—111no—
138#2501—111no—
139#1964—111no—
140#1823—111no—
141#1519—111no—
142#1282—111no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—42no—
150C23×C11—42no—
151C23×C11—81no—
152C23×C11—81no—
153C23×C11#12011yescharacteristic
154C23×C11#12111yescharacteristic
155C23×C11#12711yescharacteristic
156C23×C11C2×D812yes—
157C23×C11AGL(1,ℤ/8)12yes—
158D4×C11—42no—
159D4×C11—42no—
160D4×C11—42no—
161D4×C11—81no—
162D4×C11—82no—
163D4×C11—82no—
164D4×C11—81no—
165D4×C11—81no—
166D4×C11—81no—
167D4×C11—81no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×Dic11—24no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—44no—
187C2×Dic11—82no—
188C2×Dic11—81no—
189C2×Dic11—81no—
190C2×Dic11—81no—
191C2×Dic11—81no—
192C2×Dic11—81no—
193C8×C11—42no—
194C11⋊C8—42no—
195C2×#123—222no—
196C2×#121C2×D1111yescharacteristic
197C2×#121C2×D1111yescharacteristic
198C22×C4⋊C4—111no—
199#480—21no—
200#480—21no—
201#480—222no—
202#480—222no—
203#466—22no—
204#447—21no—
205#447—21no—
206C2×#107—221no—
207C2×#102—221no—
208C2×#99—222no—
209C2×C22⋊C8—111no—
210C2×C22⋊C8C2×D1111yescharacteristic
211#399—222no—
212#390—221no—
213#384—221no—
214#380—111no—
215C4×C22⋊C4—111no—
216#340—222no—
217#327—222no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—42no—
225C22×C11—42no—
226C22×C11—84no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—162no—
234C22×C11#39211yescharacteristic
235C22×C11#44712yes—
236C22×C11#45912yes—
237C22×C11#49311yescharacteristic
238C22×C11#49611yescharacteristic
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—81no—
243C4×C11—81no—
244C4×C11#45812yes—
245Dic11—44no—
246Dic11—82no—
247Dic11—161no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4C22⋊D1111yescharacteristic
251C22×D4C22⋊D1111yescharacteristic
252C23×C4—221no—
253C23×C4C22×D1111yescharacteristic
254C2×D8—22no—
255C22×C8—221no—
256C22×C8C22⋊D1112yes—
257#123—444no—
258#123—444no—
259#121—21no—
260#121—21no—
261#121—21no—
262#121—21no—
263#121—21no—
264#121—21no—
265#121—21no—
266#121—21no—
267C2×C4⋊C4—112no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—224no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4—221no—
275C2×C4⋊C4C22⋊D1111yescharacteristic
276C2×C4⋊C4C22⋊D1111yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—112no—
280C2×C22⋊C4—224no—
281C2×C22⋊C4—221no—
282C2×C42—221no—
283#107—22no—
284#107—224no—
285#102—22no—
286#102—22no—
287#102—224no—
288#99—444no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291C22⋊C8—112no—
292C22⋊C8—221no—
293#95—221no—
294#95—221no—
295C2×C11—22no—
296C2×C11—21no—
297C2×C11—22no—
298C2×C11—21no—
299C2×C11—161no—
300C2×C11—161no—
301C2×C11#200911yescharacteristic
302C2×C11#201111yescharacteristic
303C2×C11#202211yescharacteristic
304C24—21no—
305C24—21no—
306C24D4×D1111yescharacteristic
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—42no—
312C2×D4—42no—
313C2×D4—42no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—42no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—42no—
324C22×C4—222no—
325C22×C4—222no—
326C22×C4—442no—
327C22×C4—442no—
328C22×C4—441no—
329C22×C4—441no—
330C22×C4—441no—
331C22×C4D4×D1111yescharacteristic
332C22×C4D4×D1111yescharacteristic
333C22×C4#434111yescharacteristic
334C22×C4C2×C22⋊D1111yescharacteristic
335C22×C4C2×C22⋊D1111yescharacteristic
336C22×C4C2×C22⋊D1111yescharacteristic
337D8—82no—
338C2×C8—22no—
339C2×C8—42no—
340C2×C8—222no—
341C2×C8—442no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—222no—
347C4⋊C4—222no—
348C4⋊C4—442no—
349C4⋊C4—448no—
350C4⋊C4—441no—
351C4⋊C4—441no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—114no—
357C22⋊C4—222no—
358C22⋊C4—448no—
359C22⋊C4—442no—
360C42—442no—
361C11#995211yescharacteristic, complemented, Sylow
362C23—41no—
363C23—41no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—41no—
368C23—41no—
369C23—42no—
370C23—81no—
371C23—81no—
372C23D8×D1112yes—
373C23#6696412yes—
374C23#6699011yescharacteristic
375C23#6699211yescharacteristic
376C23#6699311yescharacteristic
377D4—42no—
378D4—42no—
379D4—42no—
380D4—81no—
381D4—82no—
382D4—81no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—82no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—224no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—444no—
401C2×C4—442no—
402C2×C4—882no—
403C2×C4—881no—
404C2×C4—881no—
405C2×C4—881no—
406C2×C4—881no—
407C2×C4—881no—
408C2×C4#6699011yescharacteristic
409C2×C4#6699111yescharacteristic
410C2×C4#6699211yescharacteristic
411C2×C4#6700611yescharacteristic
412C8—42no—
413C8—442no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—42no—
421C22—42no—
422C22—84no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—162no—
430C22#1062276312yes—
431C22#1062276411yescharacteristic
432C22#1062276711yescharacteristic
433C22#1062276912yes—
434C22#1062283611yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—81no—
439C4—81no—
440C4—444no—
441C4—882no—
442C4—1761no—
443C4#1062285612yes—
444C2—22no—
445C2—21no—
446C2—22no—
447C2—21no—
448C2—161no—
449C2—161no—
450C2#1306967311yescharacteristic
451C2#1306968511yescharacteristic
452C2#1306974511yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
Fitting, prime radicalC11×#3186C2
socleC22×C11#392
hypercenter#3186D11
hypocenterC11#9952
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3186

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10622646C2semidirect
2. #13073088C2semidirect
3. #13069453C2semidirect
4. #13068703C2semidirect
5. #13067184C2semidirect
6. #13066463C2semidirect
126. C22⋊Dic11D8semidirect
361. C11#9952semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106226462
#130730882
#130694532
#130687032
#130671842
#130664632
C11×#31862
#995211